Solving 10385 - Duathlon (Ternary search)

[andmenj-acm.git] / 11448 - Who said crisis / bigint-2007.07.07 / BigUnsigned.hh

/*
* Matt McCutchen's Big Integer Library
*/

#ifndef BIGUNSIGNED
#define BIGUNSIGNED

#include "NumberlikeArray.hh"

/*
* A BigUnsigned object represents a nonnegative integer of size
* limited only by available memory.  A BigUnsigned can be
* created from and converted back to most integral types,
* and many math operations are defined on BigUnsigneds.
*
* The number is stored as a series of blocks in a
* dynamically allocated array.  It is as if the number
* were written digit by digit in base 2 ^ N, **where N is the
* number of bits in an unsigned long.**
*
* The memory-management details that used to be in here have
* been moved into NumberlikeArray, which BigUnsigned now derives from.
* `(NlA)' means that member(s) are declared identically in NumberlikeArray.
* Such members are either redeclared here to make them public or are
* here, commented out, for reference.
*/

class BigUnsigned : protected NumberlikeArray<unsigned long> {
        
        // TYPES & CONSTANTS
        public:
        enum CmpRes { less = -1, equal = 0, greater = 1 }; // Enumeration for the result of a comparison
        typedef unsigned long Blk; // The number block type that BigUnsigneds are built from
        typedef NumberlikeArray<Blk>::Index Index; // (NlA) Type for the index of a block in the array
        NumberlikeArray<Blk>::N; // Number of bits in a Blk
        
        /*
        // FIELDS
        protected:
        Index cap; // (NlA) The current allocated capacity of this BigUnsigned (in blocks)
        Index len; // (NlA) The actual length of the number stored in this BigUnsigned (in blocks)
        Blk *blk; // (NlA) Dynamically allocated array of the number blocks
        */
        
        // MANAGEMENT
        protected:
        // These members generally defer to those in NumberlikeArray, possibly with slight changes.
        // It might be nice if one could request that constructors be inherited in C++.
        
        BigUnsigned(int, Index c) : NumberlikeArray<Blk>(0, c) {} // Creates a BigUnsigned with a capacity
        
        void zapLeadingZeros() { // Decreases len to eliminate leading zeros
                while (len > 0 && blk[len - 1] == 0)
                        len--;
        }
        
        //void allocate(Index c); // (NlA) Ensures the number array has at least the indicated capacity, maybe discarding contents
        //void allocateAndCopy(Index c); // (NlA) Ensures the number array has at least the indicated capacity, preserving its contents
        
        public:
        BigUnsigned() : NumberlikeArray<Blk>() {} // Default constructor (value is 0)
        BigUnsigned(const BigUnsigned &x) : NumberlikeArray<Blk>(x) {} // Copy constructor
        
        void operator=(const BigUnsigned &x) { // Assignment operator
                NumberlikeArray<Blk>::operator =(x);
        }
        
        BigUnsigned(const Blk *b, Index l) : NumberlikeArray<Blk>(b, l) { // Constructor from an array of blocks
                zapLeadingZeros();
        }
        
        // Constructors from integral types
        BigUnsigned(unsigned long  x);
        BigUnsigned(         long  x);
        BigUnsigned(unsigned int   x);
        BigUnsigned(         int   x);
        BigUnsigned(unsigned short x);
        BigUnsigned(         short x);
        ~BigUnsigned() {} // Destructor
        
        // CONVERTERS to integral types
        public:
        operator unsigned long () const;
        operator          long () const;
        operator unsigned int  () const;
        operator          int  () const;
        operator unsigned short() const;
        operator          short() const;
        
        // PICKING APART
        // These accessors can be used to get the pieces of the number
        public:
        NumberlikeArray<Blk>::getCapacity;
        NumberlikeArray<Blk>::getLength;
        // Note that getBlock returns 0 if the block index is beyond the length of the number.
        // A routine that uses this accessor can safely assume a BigUnsigned has 0s infinitely to the left.
        Blk getBlock(Index i) const { return i >= len ? 0 : blk[i]; }
        // Note how we replace one level of abstraction with another.  Isn't that neat?
        bool isZero() const { return NumberlikeArray<Blk>::isEmpty(); } // Often convenient for loops
        
        // COMPARISONS
        public:
        // Compares this to x like Perl's <=>
        CmpRes compareTo(const BigUnsigned &x) const;
        // Normal comparison operators
        // Bug fixed 2006.04.24: Only we, not the user, can pass a BigUnsigned off as a
        // NumberlikeArray, so we have to wrap == and !=.
        bool operator ==(const BigUnsigned &x) const {
                return NumberlikeArray<Blk>::operator ==(x);
        }
        bool operator !=(const BigUnsigned &x) const {
                return NumberlikeArray<Blk>::operator !=(x);
        }
        bool operator < (const BigUnsigned &x) const { return compareTo(x) == less   ; }
        bool operator <=(const BigUnsigned &x) const { return compareTo(x) != greater; }
        bool operator >=(const BigUnsigned &x) const { return compareTo(x) != less   ; }
        bool operator > (const BigUnsigned &x) const { return compareTo(x) == greater; }

        /*
        * BigUnsigned and BigInteger both provide three kinds of operators.
        * Here ``big-integer'' refers to BigInteger or BigUnsigned.
        *
        * (1) Overloaded ``return-by-value'' operators:
        *     +, -, *, /, %, unary -.
        * Big-integer code using these operators looks identical to
        * code using the primitive integer types.  These operators take
        * one or two big-integer inputs and return a big-integer result,
        * which can then be assigned to a BigInteger variable or used
        * in an expression.  Example:
        *     BigInteger a(1), b = 1;
        *     BigInteger c = a + b;
        *
        * (2) Overloaded assignment operators:
        *     +=, -=, *=, /=, %=, &=, |=, ^=, ++, --, flipSign.
        * Again, these are used on big integers just like on ints.
        * They take one writable big integer that both provides an
        * operand and receives a result.  The first eight also take
        * a second read-only operand.  Example:
        *     BigInteger a(1), b(1);
        *     a += b;
        *
        * (3) ``Put-here'' operations: `add', `subtract', etc.
        * Using a return-by-value or assignment operator generally involves
        * copy constructions and/or assignments.  The ``put-here'' operations
        * require none, but they are more of a hassle to use.  Most take two
        * read-only operands and save the result in the calling object `*this',
        * whose previous value is ignored.  `divideWithRemainder' is an exception.
        * <<< NOTE >>>: Put-here operations do not return a value: they don't need to!!
        * Examples:
        *     BigInteger a(43), b(7), c, d;
        *     c = a + b;   // Now c == 50.
        *     c.add(a, b); // Same effect but without the two bulk-copies.
        *     c.divideWithRemainder(b, d); // 50 / 7; now d == 7 (quotient) and c == 1 (remainder).
        *     a.add(a, b); // ``Aliased'' calls now do the right thing using a
        *              // temporary copy, but see note on divideWithRemainder.
        */
        
        // PUT-HERE OPERATIONS
        public:
        /* These 3: Two read-only operands as arguments.  Result left in *this. */
        void add(const BigUnsigned &a, const BigUnsigned &b); // Addition
        void subtract(const BigUnsigned &a, const BigUnsigned &b); // Subtraction
        void multiply(const BigUnsigned &a, const BigUnsigned &b); // Multiplication
        /* Divisive stuff
        * `a.divideWithRemainder(b, q)' is like `q = a / b, a %= b'.
        * Semantics similar to Donald E. Knuth's are used for / and %,
        * and these differ from the semantics of primitive-type
        * / and % under division by zero.
        * Look in `BigUnsigned.cc' for details.
        * `a.divideWithRemainder(b, a)' causes an exception: it doesn't make
        * sense to write quotient and remainder into the same variable.
        */
        void divideWithRemainder(const BigUnsigned &b, BigUnsigned &q);
        void divide(const BigUnsigned &a, const BigUnsigned &b) {
                BigUnsigned a2(a);
                a2.divideWithRemainder(b, *this);
                // quotient now in *this
                // don't care about remainder left in a2
        }
        void modulo(const BigUnsigned &a, const BigUnsigned &b) {
                *this = a;
                BigUnsigned q;
                divideWithRemainder(b, q);
                // remainder now in *this
                // don't care about quotient left in q
        }
        // Bitwise operations.  Result left in *this.
        // These are not provided for BigIntegers; I think that using them on BigIntegers
        // will discard the sign first.
        void bitAnd(const BigUnsigned &a, const BigUnsigned &b); // Bitwise AND
        void bitOr(const BigUnsigned &a, const BigUnsigned &b); // Bitwise OR
        void bitXor(const BigUnsigned &a, const BigUnsigned &b); // Bitwise XOR
        void bitShiftLeft(const BigUnsigned &a, unsigned int b); // Bitwise left shift
        void bitShiftRight(const BigUnsigned &a, unsigned int b); // Bitwise right shift
        
        // NORMAL OPERATORS
        // These perform the operation on this (to the left of the operator)
        // and x (to the right of the operator) and return a new BigUnsigned with the result.
        public:
        BigUnsigned operator +(const BigUnsigned &x) const; // Addition
        BigUnsigned operator -(const BigUnsigned &x) const; // Subtraction
        BigUnsigned operator *(const BigUnsigned &x) const; // Multiplication
        BigUnsigned operator /(const BigUnsigned &x) const; // Division
        BigUnsigned operator %(const BigUnsigned &x) const; // Modular reduction
        BigUnsigned operator &(const BigUnsigned &x) const; // Bitwise AND
        BigUnsigned operator |(const BigUnsigned &x) const; // Bitwise OR
        BigUnsigned operator ^(const BigUnsigned &x) const; // Bitwise XOR
        BigUnsigned operator <<(unsigned int b) const; // Bitwise left shift
        BigUnsigned operator >>(unsigned int b) const; // Bitwise right shift
        // Additional operators in an attempt to avoid overloading tangles.
        BigUnsigned operator <<(int b) const;
        BigUnsigned operator >>(int b) const;
        
        // ASSIGNMENT OPERATORS
        // These perform the operation on this and x, storing the result into this.
        public:
        void operator +=(const BigUnsigned &x); // Addition
        void operator -=(const BigUnsigned &x); // Subtraction
        void operator *=(const BigUnsigned &x); // Multiplication
        void operator /=(const BigUnsigned &x); // Division
        void operator %=(const BigUnsigned &x); // Modular reduction
        void operator &=(const BigUnsigned &x); // Bitwise AND
        void operator |=(const BigUnsigned &x); // Bitwise OR
        void operator ^=(const BigUnsigned &x); // Bitwise XOR
        void operator <<=(unsigned int b); // Bitwise left shift
        void operator >>=(unsigned int b); // Bitwise right shift
        // Additional operators in an attempt to avoid overloading tangles.
        void operator <<=(int b);
        void operator >>=(int b);
        
        // INCREMENT/DECREMENT OPERATORS
        // These increase or decrease the number by 1.  To discourage side effects,
        // these do not return *this, so prefix and postfix behave the same.
        public:
        void operator ++(   ); // Prefix  increment
        void operator ++(int); // Postfix decrement
        void operator --(   ); // Prefix  increment
        void operator --(int); // Postfix decrement
        
        // Helper function that needs access to BigUnsigned internals
        friend Blk getShiftedBlock(const BigUnsigned &num, Index x, unsigned int y);
};

// NORMAL OPERATORS
/* These create an object to hold the result and invoke
* the appropriate put-here operation on it, passing
* this and x.  The new object is then returned. */
inline BigUnsigned BigUnsigned::operator +(const BigUnsigned &x) const {
        BigUnsigned ans;
        ans.add(*this, x);
        return ans;
}
inline BigUnsigned BigUnsigned::operator -(const BigUnsigned &x) const {
        BigUnsigned ans;
        ans.subtract(*this, x);
        return ans;
}
inline BigUnsigned BigUnsigned::operator *(const BigUnsigned &x) const {
        BigUnsigned ans;
        ans.multiply(*this, x);
        return ans;
}
inline BigUnsigned BigUnsigned::operator /(const BigUnsigned &x) const {
        BigUnsigned ans;
        ans.divide(*this, x);
        return ans;
}
inline BigUnsigned BigUnsigned::operator %(const BigUnsigned &x) const {
        BigUnsigned ans;
        ans.modulo(*this, x);
        return ans;
}
inline BigUnsigned BigUnsigned::operator &(const BigUnsigned &x) const {
        BigUnsigned ans;
        ans.bitAnd(*this, x);
        return ans;
}
inline BigUnsigned BigUnsigned::operator |(const BigUnsigned &x) const {
        BigUnsigned ans;
        ans.bitOr(*this, x);
        return ans;
}
inline BigUnsigned BigUnsigned::operator ^(const BigUnsigned &x) const {
        BigUnsigned ans;
        ans.bitXor(*this, x);
        return ans;
}
inline BigUnsigned BigUnsigned::operator <<(unsigned int b) const {
        BigUnsigned ans;
        ans.bitShiftLeft(*this, b);
        return ans;
}
inline BigUnsigned BigUnsigned::operator >>(unsigned int b) const {
        BigUnsigned ans;
        ans.bitShiftRight(*this, b);
        return ans;
}
inline BigUnsigned BigUnsigned::operator <<(int b) const {
        if (b < 0)
                throw "BigUnsigned::operator <<(int): Negative shift amounts are not supported";
        return *this << (unsigned int)(b);
}
inline BigUnsigned BigUnsigned::operator >>(int b) const {
        if (b < 0)
                throw "BigUnsigned::operator >>(int): Negative shift amounts are not supported";
        return *this >> (unsigned int)(b);
}

/*
 * ASSIGNMENT OPERATORS
 * 
 * Now the responsibility for making a temporary copy if necessary
 * belongs to the put-here operations.  I made this change on 2007.02.13 after
 * Boris Dessy pointed out that the old implementation handled calls like
 * "a *= a" badly: it translated them to essentially "a.multiply(aCopy, a)",
 * which threw an exception.
 */
inline void BigUnsigned::operator +=(const BigUnsigned &x) {
        add(*this, x);
}
inline void BigUnsigned::operator -=(const BigUnsigned &x) {
        subtract(*this, x);
}
inline void BigUnsigned::operator *=(const BigUnsigned &x) {
        multiply(*this, x);
}
inline void BigUnsigned::operator /=(const BigUnsigned &x) {
        // Updated for divideWithRemainder
        BigUnsigned thisCopy(*this);
        thisCopy.divideWithRemainder(x, *this);
        // quotient left in *this
        // don't care about remainder left in thisCopy
}
inline void BigUnsigned::operator %=(const BigUnsigned &x) {
        // Shortcut (woohoo!)
        BigUnsigned q;
        divideWithRemainder(x, q);
        // remainder left in *this
        // don't care about quotient left in q
}
inline void BigUnsigned::operator &=(const BigUnsigned &x) {
        bitAnd(*this, x);
}
inline void BigUnsigned::operator |=(const BigUnsigned &x) {
        bitOr(*this, x);
}
inline void BigUnsigned::operator ^=(const BigUnsigned &x) {
        bitXor(*this, x);
}
inline void BigUnsigned::operator <<=(unsigned int b) {
        bitShiftLeft(*this, b);
}
inline void BigUnsigned::operator >>=(unsigned int b) {
        bitShiftRight(*this, b);
}
inline void BigUnsigned::operator <<=(int b) {
        if (b < 0)
                throw "BigUnsigned::operator <<=(int): Negative shift amounts are not supported";
        *this <<= (unsigned int)(b);
}
inline void BigUnsigned::operator >>=(int b) {
        if (b < 0)
                throw "BigUnsigned::operator >>=(int): Negative shift amounts are not supported";
        *this >>= (unsigned int)(b);
}

#endif